BP Chats

Is it unheard of for a player to make it to the major leagues and stick at age 31? I am asking because of Chase Lambin, who is hitting very well at Syracuse, but has never made the bigs yet. I am not thinking about him being a starter somewhere or anything, but knowing that nobody is a prospect anymore at that age, would somebody like Lambin be playing to finally at least get the cup of coffee? Or is it realistic to maybe get that one big paycheck?(HalfStreet from Fairfax VA)